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see what the predictions of these assumptions for the real part are.Having to introduce a subtraction into (2), we therefore replace it byA {v) = v2_v2 + 22 f dv ' 22k2 2OD ' ~' i+ -- f dv + c - (3)2' K k'(v'2 - v2}- i) + ?(2Note that, instead of performing a subtraction on the entire inte-gral, we divide it into two parts. One is written in an unsubtractedform, and the other in a subtracted one. This is done for practicalpurposes. It avoids stressing the low-energy input and thus increasingthe errors in the calculation. The number c depends on the choice of K.Equation (3) also demonstrates the fact that the real part at low energyis not necessarily affected by the new assumptions on the high-energybehavior. We are actually able to reproduce at low energies (say, below4 BeV) the same results previously obtained by the use of (2) with anyreasonably decreasing fit to aTo illustrate the changes brought about by the assumptions on thebehavior of the total cross section, let us discuss a mathematicalexample that is very similar to the actual situation in K-p. Let usdenote the two reactions in question by A and B (analogous to Kp andK p respectively). Assume first that (case I):ImA =aiv , Im B =av+b4v , O<v<oD . (4)It is then easy to find that